A129295 Numbers m such that m^3 - 1 has no divisors d with 1 < d < m - 1.

3, 4, 6, 8, 12, 14, 20, 24, 38, 54, 62, 80, 90, 110, 138, 150, 164, 168, 192, 194, 272, 278, 314, 332, 348, 398, 402, 434, 500, 572, 642, 644, 720, 728, 762, 798, 812, 860, 864, 878, 920, 992, 1020, 1022, 1070, 1092, 1098, 1118, 1130, 1182, 1202, 1230, 1260, 1308

Offset: 1

Author

Reinhard Zumkeller, Apr 09 2007

Keywords

• nonn

Comments

Numbers m such that A129294(m) = #{1,m-1} = 2.

Essentially the same as A096175. Note that m^3 - 1 = (m - 1)*(m^2 + m + 1), so m - 1 must be prime. For m > 4, the smallest divisor > 1 of m^2 + m + 1 is no larger than sqrt(m^2 + m + 1) < m + 1 unless m^2 + m + 1 is also prime. Also note that gcd(m, m^2 + m 1 ) = gcd(m - 1, m^2 + m + 1) = 1, so m^2 + m + 1 must also be prime, making m^3 - 1 a semiprime. - Jianing Song, Aug 01 2018

Examples

			{1,11,157,1727} is the set of divisors of 12^3 - 1, therefore 12 is a term, since A129294(12) = #{1,11} = 2.
		

Crossrefs

Cf. A096175, A129293, A129294.

Formula

a(n) = A096175(n-2) for n > 2. - Jianing Song, Aug 01 2018